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Tuning systems for qanun: Difference between revisions

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**Imported revision 247611749 - Original comment: **
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**Imported revision 247616689 - Original comment: **
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<h2>IMPORTED REVISION FROM WIKISPACES</h2>
<h2>IMPORTED REVISION FROM WIKISPACES</h2>
This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
: This revision was by author [[User:hstraub|hstraub]] and made on <tt>2011-08-22 05:52:15 UTC</tt>.<br>
: This revision was by author [[User:hstraub|hstraub]] and made on <tt>2011-08-22 06:24:25 UTC</tt>.<br>
: The original revision id was <tt>247611749</tt>.<br>
: The original revision id was <tt>247616689</tt>.<br>
: The revision comment was: <tt></tt><br>
: The revision comment was: <tt></tt><br>
The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>
The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>
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University.
University.


=Explanation=
The tuning tables on this page are specifically designed for the tuning system of the [[qanun]] (see the link for details on the system of tuning and playing a qanun with "mandals/orabs").
The tuning tables on this page are specifically designed for the tuning system of the [[qanun]] (see the link for details on the system of tuning and playing a qanun with "mandals/orabs").
The possible pitches of a string obtained via raising/lowering the mandals/orabs lie within one [[2187_2048|apotome (2187/2048, 113.7 cents)]]. All systems use 8 mandals, allowing a subdivision of the apotome into 7 parts.
The first rough subdivision of the apotome is always into one [[81_80|syntonic comma (81/80, 21.5 cents)]], one [[25_24|Zarlinian semitone (25/24, 70.7 cents)]] and another syntonic comma. The middle part (Zarlinian semitone) is then further subdivided into 5 (unequal or equal) parts. The various systems differ mainly in the division of the middle part.
=Explanation of the tuning tables=


The whole table covers roughly the range of a fourth (the range where the ajnas - maqam tetrachords - reside). Each row corresponds to one string of the qanun. In the first column stands the basic (relative) tuning of a string while the following columns indicate possible intervals that can be reached via lowering the mandals/orabs.
The whole table covers roughly the range of a fourth (the range where the ajnas - maqam tetrachords - reside). Each row corresponds to one string of the qanun. In the first column stands the basic (relative) tuning of a string while the following columns indicate possible intervals that can be reached via lowering the mandals/orabs.
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=Older systems=  
=Older systems=  
==First System J.J.Weiss==  
==First System J.J.Weiss==  
Inequal subdivision of the [[2187_2048|apotome (2187/2048, 113.7 cents)]] into 7 parts (8 mandals/orabs), in the following manner:
Subdivision of 25/24 into 65/64 (26 cents), 144/143 (12 cents) and 55/54 (32 cents).
* Subdivision into one [[81_80|syntonic comma (81/80, 21.5 cents)]], one [[25_24|Zarlinian semitone (25/24, 70.7 cents)]] and another syntonic comma.
65/64 and 55/54 are each split into two.
* Further subdivision of 25/24 into 65/64 (26 cents), 144/143 (12 cents) and 55/54 (32 cents).
* 65/64 and 55/54 are each split into two.


This gives the following interval positions of the mandals: 22, 13, 13, 12, 16, 16, 22 cents.
This gives the following interval positions of the mandals: 22, 13, 13, 12, 16, 16, 22 cents.
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===Equal division of the Zarlinian semitone===  
===Equal division of the Zarlinian semitone===  
J.J. Weiss
J.J. Weiss
Subdivision of the apotome (2187/2048, 113.7 cents) into one syntonic comma, one Zarlinian semitone ([[25_24|25/24, 70.67 cents]]) and another syntonic comma as in the other systems, and then an equal division of the Zarlinian semitone into 5 parts.
This is the simplest variant for luthiers...
Advantage: easier for luthiers.


Mandal positions (cents): &lt;span style="color: #00000a; font-family: Tahoma;"&gt;22|14|14|14|14|14|22&lt;/span&gt;
Mandal positions (cents): &lt;span style="color: #00000a; font-family: Tahoma;"&gt;22|14|14|14|14|14|22&lt;/span&gt;
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<h4>Original HTML content:</h4>
<h4>Original HTML content:</h4>
<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;width:200%;white-space: pre-wrap ! important" class="old-revision-html">&lt;html&gt;&lt;head&gt;&lt;title&gt;tuning systems for qanun&lt;/title&gt;&lt;/head&gt;&lt;body&gt;&lt;span style="font-size: 150%;"&gt;&lt;strong&gt;Tuning systems for the qanun&lt;/strong&gt;&lt;/span&gt;&lt;br /&gt;
<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;width:200%;white-space: pre-wrap ! important" class="old-revision-html">&lt;html&gt;&lt;head&gt;&lt;title&gt;tuning systems for qanun&lt;/title&gt;&lt;/head&gt;&lt;body&gt;&lt;span style="font-size: 150%;"&gt;&lt;strong&gt;Tuning systems for the qanun&lt;/strong&gt;&lt;/span&gt;&lt;br /&gt;
&lt;!-- ws:start:WikiTextTocRule:38:&amp;lt;img id=&amp;quot;wikitext@@toc@@normal&amp;quot; class=&amp;quot;WikiMedia WikiMediaToc&amp;quot; title=&amp;quot;Table of Contents&amp;quot; src=&amp;quot;/site/embedthumbnail/toc/normal?w=225&amp;amp;h=100&amp;quot;/&amp;gt; --&gt;&lt;div id="toc"&gt;&lt;h1 class="nopad"&gt;Table of Contents&lt;/h1&gt;&lt;!-- ws:end:WikiTextTocRule:38 --&gt;&lt;!-- ws:start:WikiTextTocRule:39: --&gt;&lt;div style="margin-left: 1em;"&gt;&lt;a href="#Explanation"&gt;Explanation&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:start:WikiTextTocRule:38:&amp;lt;img id=&amp;quot;wikitext@@toc@@normal&amp;quot; class=&amp;quot;WikiMedia WikiMediaToc&amp;quot; title=&amp;quot;Table of Contents&amp;quot; src=&amp;quot;/site/embedthumbnail/toc/normal?w=225&amp;amp;h=100&amp;quot;/&amp;gt; --&gt;&lt;div id="toc"&gt;&lt;h1 class="nopad"&gt;Table of Contents&lt;/h1&gt;&lt;!-- ws:end:WikiTextTocRule:38 --&gt;&lt;!-- ws:start:WikiTextTocRule:39: --&gt;&lt;div style="margin-left: 1em;"&gt;&lt;a href="#Explanation of the tuning tables"&gt;Explanation of the tuning tables&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:39 --&gt;&lt;!-- ws:start:WikiTextTocRule:40: --&gt;&lt;div style="margin-left: 1em;"&gt;&lt;a href="#Older systems"&gt;Older systems&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:39 --&gt;&lt;!-- ws:start:WikiTextTocRule:40: --&gt;&lt;div style="margin-left: 1em;"&gt;&lt;a href="#Older systems"&gt;Older systems&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:40 --&gt;&lt;!-- ws:start:WikiTextTocRule:41: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Older systems-First System J.J.Weiss"&gt;First System J.J.Weiss&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:40 --&gt;&lt;!-- ws:start:WikiTextTocRule:41: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Older systems-First System J.J.Weiss"&gt;First System J.J.Weiss&lt;/a&gt;&lt;/div&gt;
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University.&lt;br /&gt;
University.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:0:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc0"&gt;&lt;a name="Explanation"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;Explanation&lt;/h1&gt;
The tuning tables on this page are specifically designed for the tuning system of the &lt;a class="wiki_link" href="/qanun"&gt;qanun&lt;/a&gt; (see the link for details on the system of tuning and playing a qanun with &amp;quot;mandals/orabs&amp;quot;).&lt;br /&gt;
The tuning tables on this page are specifically designed for the tuning system of the &lt;a class="wiki_link" href="/qanun"&gt;qanun&lt;/a&gt; (see the link for details on the system of tuning and playing a qanun with &amp;quot;mandals/orabs&amp;quot;).&lt;br /&gt;
&lt;br /&gt;
The possible pitches of a string obtained via raising/lowering the mandals/orabs lie within one &lt;a class="wiki_link" href="/2187_2048"&gt;apotome (2187/2048, 113.7 cents)&lt;/a&gt;. All systems use 8 mandals, allowing a subdivision of the apotome into 7 parts.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
The first rough subdivision of the apotome is always into one &lt;a class="wiki_link" href="/81_80"&gt;syntonic comma (81/80, 21.5 cents)&lt;/a&gt;, one &lt;a class="wiki_link" href="/25_24"&gt;Zarlinian semitone (25/24, 70.7 cents)&lt;/a&gt; and another syntonic comma. The middle part (Zarlinian semitone) is then further subdivided into 5 (unequal or equal) parts. The various systems differ mainly in the division of the middle part.&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:0:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc0"&gt;&lt;a name="Explanation of the tuning tables"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;Explanation of the tuning tables&lt;/h1&gt;
&lt;br /&gt;
The whole table covers roughly the range of a fourth (the range where the ajnas - maqam tetrachords - reside). Each row corresponds to one string of the qanun. In the first column stands the basic (relative) tuning of a string while the following columns indicate possible intervals that can be reached via lowering the mandals/orabs.&lt;br /&gt;
The whole table covers roughly the range of a fourth (the range where the ajnas - maqam tetrachords - reside). Each row corresponds to one string of the qanun. In the first column stands the basic (relative) tuning of a string while the following columns indicate possible intervals that can be reached via lowering the mandals/orabs.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
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&lt;!-- ws:start:WikiTextHeadingRule:2:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc1"&gt;&lt;a name="Older systems"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:2 --&gt;Older systems&lt;/h1&gt;
&lt;!-- ws:start:WikiTextHeadingRule:2:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc1"&gt;&lt;a name="Older systems"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:2 --&gt;Older systems&lt;/h1&gt;
  &lt;!-- ws:start:WikiTextHeadingRule:4:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc2"&gt;&lt;a name="Older systems-First System J.J.Weiss"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:4 --&gt;First System J.J.Weiss&lt;/h2&gt;
  &lt;!-- ws:start:WikiTextHeadingRule:4:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc2"&gt;&lt;a name="Older systems-First System J.J.Weiss"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:4 --&gt;First System J.J.Weiss&lt;/h2&gt;
  Inequal subdivision of the &lt;a class="wiki_link" href="/2187_2048"&gt;apotome (2187/2048, 113.7 cents)&lt;/a&gt; into 7 parts (8 mandals/orabs), in the following manner:&lt;br /&gt;
  Subdivision of 25/24 into 65/64 (26 cents), 144/143 (12 cents) and 55/54 (32 cents).&lt;br /&gt;
&lt;ul&gt;&lt;li&gt;Subdivision into one &lt;a class="wiki_link" href="/81_80"&gt;syntonic comma (81/80, 21.5 cents)&lt;/a&gt;, one &lt;a class="wiki_link" href="/25_24"&gt;Zarlinian semitone (25/24, 70.7 cents)&lt;/a&gt; and another syntonic comma.&lt;/li&gt;&lt;li&gt;Further subdivision of 25/24 into 65/64 (26 cents), 144/143 (12 cents) and 55/54 (32 cents).&lt;/li&gt;&lt;li&gt;65/64 and 55/54 are each split into two.&lt;/li&gt;&lt;/ul&gt;&lt;br /&gt;
65/64 and 55/54 are each split into two.&lt;br /&gt;
&lt;br /&gt;
This gives the following interval positions of the mandals: 22, 13, 13, 12, 16, 16, 22 cents.&lt;br /&gt;
This gives the following interval positions of the mandals: 22, 13, 13, 12, 16, 16, 22 cents.&lt;br /&gt;
Luthier: Ejder Gulec&lt;br /&gt;
Luthier: Ejder Gulec&lt;br /&gt;
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&lt;!-- ws:start:WikiTextHeadingRule:24:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc12"&gt;&lt;a name="Newer systems-Symmetrical and super-symmetrical models-Equal division of the Zarlinian semitone"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:24 --&gt;Equal division of the Zarlinian semitone&lt;/h3&gt;
&lt;!-- ws:start:WikiTextHeadingRule:24:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc12"&gt;&lt;a name="Newer systems-Symmetrical and super-symmetrical models-Equal division of the Zarlinian semitone"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:24 --&gt;Equal division of the Zarlinian semitone&lt;/h3&gt;
  J.J. Weiss&lt;br /&gt;
  J.J. Weiss&lt;br /&gt;
Subdivision of the apotome (2187/2048, 113.7 cents) into one syntonic comma, one Zarlinian semitone (&lt;a class="wiki_link" href="/25_24"&gt;25/24, 70.67 cents&lt;/a&gt;) and another syntonic comma as in the other systems, and then an equal division of the Zarlinian semitone into 5 parts.&lt;br /&gt;
This is the simplest variant for luthiers...&lt;br /&gt;
Advantage: easier for luthiers.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Mandal positions (cents): &lt;span style="color: #00000a; font-family: Tahoma;"&gt;22|14|14|14|14|14|22&lt;/span&gt;&lt;br /&gt;
Mandal positions (cents): &lt;span style="color: #00000a; font-family: Tahoma;"&gt;22|14|14|14|14|14|22&lt;/span&gt;&lt;br /&gt;
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